Phương pháp kích thích năng lực tư duy cho học sinh phổ thông trong dạy học giải toán : Đề tài NCKH: QS 05 02

- Ve phucmg phdp cu the Cong trinh da sir dung phuang phap nghien cuu tai lieu, di6u tra, quan sat, phan tich, t6ng hap, so sanh, khai quat hoa de nhan ra cac uu nhuac diem cua n6i dung

DAI HOC QUOC GIA HA NOI

KHOA SU PHAM

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Thae Si BUI THI HUCING

PHirONG PHAP KICH THICH NANG Ll/C TlT DUY

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CHO HOC SINH PHO THONG TRONG

DAY HOC GIAI TOAN

Mdso:QS.05.02

DM HOC QUOC GIA HA NOI

TRUNG TAM THONG TIN THU VIEN

DT / 94-^

Ha Npi, 3/2008

MUC LUC

Mdddu I

Noi dung 5

Chuang 1: CO Sd KHOA HOC Vl^

KICH THICH NANG LlTC TlTDUY CHO NG\J6l HOC 5

1.1 M6t so net caban cua qua trinh day hpc 5

1.1.1 Quan niem ve hpc va day each hpc 5

1.1.2 Quan niem ve day hpc tich cue 7

1.2 Phuang phap bien doi chat luong tuduy cua ngudi hpc 8

1.2.1 Mot so khai niem lien quan tdi tuduy 8

1.2.2 Mot sophucfng thiic ton tai cua tuduy 13

1.2.3 Phuang phap bien doi chat luang tuduy cua nguoi hoc 16

Chuang 2 : M 6 I QUAN QUAN HE GltTA

DAY HOC GIAI TOAN V&I SlT PHAT TRIEN NANG LiTC TtfDUY 27

2.1 Ban chat cua day hoc giai toan a nha trircmg pho thong 27

2.1.1 Tam quan trpng cua day hpc giai toan a truang pho thong 27

2.1.2 Quan niem ve giai toan vaday hpc giai toan 28

2.1.3 Cac budc trong day hpc giai toan 32

2.2 Tac dong tu-ong ho gifra boat dong giai toan voi ron luyen, boi du-ong,

phat trien nang lire t u d u y cua hoc sinh 32

2,2A Nang luc tu duy can thiet trong tung buoc

ciia boat dong giai toan 32

2.2.2 Hinh thanh, ren luyen, boi duong pham chat tri tue toan hpc cho hpc

sinh thong qua day hpc giai toan 35

Chuang 3 : PHl/ONG PHAP KICH THICH NANG Life TlTDUY

CHO HOC SINH PHO THONG TRONG DAY HOC GIAI TOAN, 46

3.1 De xuat phuong phap 46

3.1.1 Xac dinh dp kho cua cac bai toan dua ra phu hop voi doi tuang nguoi

hpc 46 3.1.2 Nang cao long tu tin cho hpc sinh vao kha nang nhan thuc toan hpc cua

hp; tung buac giup cac em tu tim ra lai giai cac bai toan 51

3.1.3 Bien npi day hpc giai toan (neu co the) tro thanh cac dang tro choi vui

ve , thoa mai nhung van nham vao muc tieu day 56

3.L4 Giiip hpc sinh nhan ra cai hay, cai dep cai thu vi cua toan hpc ciing

nhung ung dung thuc tien cua n6 58

3.1.5 Sudung cong nghe thong tin tro tro viec day hpc giai toan 62

3.2 To chirc thuc nghiein va danh gia ket qua 64

Ket luan 91

Cac ky hieu viet tat

Viet ddy du Viet tdt

Dai hpc Quoc Gia DHQG Giao su tien sT GS.TS Nha xuat ban Nxb Trung hoc pho thong THPT

Tien sT khoa hoc TS KH

tri thirc tra thanh cot I5i cua sir tien bp xa hpi Trong kinh ti tri thuc, ngudn

nhan luc ngay cang doi hoi duoc nang cao ve tri tue va sir nhay cam; vi the vai tro tu duy cua moi ca nhan tra thanh dong lire phat trien cua dan toe va thai dai De dap img duac nhu cau d6, van de chat luang tu duy cua hpc sinh, sinh vien phai duac dat len hang dau

Mon toan duac coi la mot trong nhung mon hpc quan trpng giup ma

mang tri tue va phat trien tu duy 16 gic cho Icrp tre Trong day hpc toan a bac

hpc pho thong, hoat dong giai toan la ca hpi tot nha't de hpc sinh duac van dung, bpc 16 va phat trien kha nang sang tao qua qua trinh dem nhimg tri thirc toan hpc da duac trang bi vao giai cac bai toan cung nhu giai quyet cac van de trong cupc song thuc ti6n lien quan toi toan hpc

De phat huy vai tro cua viec day hpc giai toan, dieu quan trpng can chii y

la phuang phap va nghe thuat dieu khien cua Thay, to chirc sao cho hpc sinh tham gia vao cac hoat dong giai toan mot each tich cue, thoa mai

Song, hien nay a cac trucmg pho thong, viec day hpc giai toan con nhi6u

ba't cap Hpc sinh duang nhu bi khuon vao viec giai cac bai toan theo mot trinh

tu nhat dinh, lap di lap lai nhu mot nhiem vu quen thupc dien ra hang ngay nen cac em thuang hay chan nan va mat di tinh chu dong sang tao Con ve phia giao vien lai chi chu trpng den dap so, ket qua cua bai toan cu the han la day hpc sinh biet phan tich de tim ra each giai bai toan; biet nhan xet danh gia mot

bai toan di r6i tijf do sang tao each giai quyet cac bai toan khac Vdi each day

do, v6 tinh da lam giam di kha nang sang tao dang tiSm an trong hpc sinh Tir tinh hinh cu the d6, da dat ra yeu cau nghien cuu de tim ra phuang phap moi trong day hpc giai toan nham kich thich nang luc tu duy cho hpc sinh pho thdng la va'n de cap thiet

2 Muc tieu nghien curu

Cong trinh nham tim ra phuang phap de kich thich nang luc tu duy cho hpc sinh pho thong trong day hpc sinh giai toan va ung dung vao trong day hpc m6t s6' dang toan cu the; tijf do gop phan nang cao nang luc giai toan, kha nang tim toi, sang tao, gay hung thu trong hpc tap toan cho hpc sinh

3 Doi tutfng nghien cuu

Phuang phap de kich thich nang luc tu duy cho hpc sinh pho thong trong day hpc sinh giai toan

4 Nhiem vu nghien cuu

- Nghien curu ca sa khoa hpc ve tu duy, cac phucmg phap tu duy, ngoai luc, npi luc va nhung pham vi thupc phuang phap kich thich nang luc tu duy cho nguai hpc

- Tim hieu moi quan he bien chung giira hoat dong giai toan voi sir phat triln nang luc tu duy cho hpc sinh pho thong,

- De xuat cac phuang phap kich thich nang luc tu duy cho hpc sinh pho thong trong day hpc giai toan ciing cac bai giang minh hoa

- T6 chuc thuc nghiem va danh gia ket qua

5 PhuoTig phap nghien cuu

- Ve phucmg phdp cu the

Cong trinh da sir dung phuang phap nghien cuu tai lieu, di6u tra, quan sat, phan tich, t6ng hap, so sanh, khai quat hoa de nhan ra cac uu nhuac diem cua n6i dung va phuang phap day hpc giai toan a pho thong hien nay; tir do de xua't phuang phap day mdi nham kich thich nang luc tu duy cho hpc sinh va trien khai thuc nghi6m de khang dinh ket qua nghien cim

6 Ket qua nghien cuu va y nghla cong trinh

- Lam sang to ca so khoa hpc cua viec kich thich nang lire tu duy cho nguai hpc noi chung va day hpc giai toan a pho thong noi rieng,

- D^ xua't duac phuang phap kich thich nang luc tu duy cho hpc sinh pho thong trong day hpc giai toan cimg vai nhimg bai giang minh hpa

- Cong trinh da duac the hien trong hai bai bao

- Cong trinh co the lam tai lieu tham khao cho giao vien day toan a pho thong va cho sinh vien su pham toan

7.Cau true cua de tai

Ngoai phan ma dau va ket luan cung cac danh muc tai lieu tham khao, cong trinh duac chia thanh 3 chuang:

Chuomg 1

CO S6 KHOA HOC VE

KICH THICH NANG LlTC T U D U Y CHO NGU^ClI HOC

7.7 Mot so net ca bdn cua qud trinh day hgc

1.1.1 Quan niem ve hpc va day each hpc

1.1.2 Quan niem ve day hpc tich cue

1.2 Phuang phap bien doi chat luang tu duy cua nguci hpc

1.2.1 Mot so khai niem lien quan tdi tuduy

1.2.2 Mot so phuang thu'c ton tai cua tu duy

1.2.3 Phuang phap bien doi chat luang tu duy ciia nguci hpc

2.1.1 Tam quan trpng cua day hpc giai toan a truang pho thong

2.1.2 Quan niem v6 giai toan va day hpc giai toan

2.1.3 Cac bu6c trong day hpc giai toan

2.2 Tdc dgng tirang ho giira hoat dgng gidi todn vai ren luyen, boi duong,

phdt trien ndng luc tu duy cua hgc sinh

2.2.1 Nang lire tu duy can thiet trong timg buac cua hoat dong giai toan

2.2.2 Hinh thanh, ren luyen, boi duang pham chat tri tue toan hpc cho

hpc sinh thong qua day hpc giai toan

Chuang 3

PHirONG PHAP KICH THICH NANG LU^C Tlf DUY

CHO HOC SINH PHO THONG TRONG DAY HOC GIAI TOAN

3.1 De xudt phuang phdp

Trong ph4n nay cong trinh da dua ra phuang phap chung va cac bien cu the

de kich thich nang lire cho hpc sinh pho thong trong day hpc giai toan ciing vi

du minh hpa cho timg bien phap

3.2 To chuc thuc nghiem vd ddnh gid ket qud

PHAN NOI DUNG

•

Chuong 1

CO SO KHOA HOC VE KICH THICH NANG LUC TUDUY CHO NGUdi HOC

1.1 Mot so net ca ban cua qua trinh day hoc

7.7.7 Quan niem ve hgc vd day cdch hgc

Hgc va day each hpc la mot van de ca ban cua bat cu* nen giao due nao

Mot da't nu6c duac gpi la nude co nen giao due phat trien phu thupc rat nhieu vao each hpc va day each hpc trong tat ca cac nha trudng, dac biet la d nha trucmg pho th6ng Do do, viec hieu diing ban chat cua qua trinh day hpc co y nghia quan trpng trong dinh hudng cho su phat trien nen giao due nude nha Chinh vi the, dieu trude tien cdng trinh muon duac diem qua cac quan niem khac nhau ve day va hpc tir xua den nay

Qua nghien cuu, chiing ta thay: day hpc cd tir thdi co dai Hy Lap (tiic la the ky thu* V trude cdng nguyen) Ngudi md trudng day hpc cd bai ban d^u

tien la Platon {427-347 truac CN) Ong md trudng tai khu rimg gan thanh

Aten; Day la khu rimg nhan dan Hy Lap trong de tudng niem than Academ, nen trudng cd ten la Academi, v6 sau cac vien Ham Lam cua cac nude tren the gidi deu lay ten la Academic

Trude kia, Platon cho rSng: '' Day hgc la mot cdch kich thich linh h6n'\

Quan niem nay xua't phat tir ca sd triet hpc coi con ngudi cd hai phan : phan

The xac (do tinh yeu giua cha vd me tgo ra) va phan Linh hon {do Trai phdi

nhap vdo) Linh hon dau tien d vdi thuang de cho nen linh hon am hieu moi

chuyen Nhung khi nhap vao than xac dudi ha gidi, linh hon quen het Nhiem

vu cua cua ngudi thay la kich thich linh hon dd nhd lai nhirng dieu hieu biet sau sac ngay tir kiep trude Vdi quan niem dd, ngudi ta sinh ra ai cung cd the

gioi duac Hp khdng gidi duac la do th^y giao chua biet each kich thich linh h6n hp Anh hudng cua quan niem nay da dan den nhi6u y kien eho rang:

" Thdy nao, trd ndy ! "

Cang ngay khoa hpc cang phat trien, eon ngudi cang chii y nhieu den nang luc nhan thu'c cua ban than mdi ca nhan Khoa hpc da chung minh rang, ngoai cac yeu td sinh hpc, chi sd zen thong minh da anh hudng rat ldn den viec

hpc tap cua mdi ca nhan Tijr dd, cung xua't hien nhieu quan niem khac nhau \i

day va hpc:

- Quan niem truyen thdng cho rang: Day la truyen thu kien thuc cua ngudi th^y cho trd, cdn hoc la sir linh hpi kien thuc cua trd Quan niem nay da theo sudt qua trinh day hpc trong nha trudng pho thong d nude ta nhieu nam trude day va cang ngay bpc 16 nhuac di6m ciia nd,

Ngoai quan niem truyen thdng d tren, cdn cd rat nhieu y kien khac nhau cua cac nha khoa hpc ve vah de nay Xin dan cir mot sd y kien:

Y kien cua GS Nguyen Nggc Quang:

- Hgc la boat dong vdi ddi tuang, trong dd hpc sinh la chii the, khai niem

khoa hpc la ddi tuang de chiem linh Hgc la qua trinh tu giac tich cue, tu lire

chiem linh khai niem khoa hpc dudi su dieu khien su pham cua giao vien

- Day la dieu khien tdi uu hoa qua trinh hpc sinh chiem linh khai niem

khoa hpc va bang each dd, phat trien hinh thanh nhan each [3,93-95]

Y kien cua GS.TSKH Lam Quan Thiep

- Hgc la qua trinh tu bien doi minh va lam phong phii minh bang each

chpn nhap va xir ly thong tin lay tir moi trudng xung quanh

- Day la viec giiip cho ngudi hpc tu minh chiem linh nhung kien thirc, ky

nang va hinh thanh hoac lam bien doi tinh cam, thai dp [3,147]

Quan diem cua Luu Xuan Mdi

Trong sach Ly luan day hgc eiia chinh tac gia da viet: "Ban chat cua qua

trinh day hpc la qua trinh nhan thiic cua hpc sinh, sinh vien"

Cac quan diem tren, tuy duac trinh bay dudi nhieu hinh thirc khac nhau,

nhung d6u muon khang dinh rang, qua trinh day hpc la mot he ven toan bao

gom nhieu thanh to luon lu6n tuang tae vdi nhau theo nhung quy luat rieng, tham nhap vao nhau, quy dinh lan nhau de tao nen su thdng nhat bien chiing

giOa hai boat dong, ciia hai ehu the Thdy va tro,

Cac quan diem tren d^u ed xu hudng muon vuat qua quan diem day hpc truyen thdng, vi each day va hpc truyen thdng ed nhirng nhuac diem rat ldn Vdi each day hoc truydn thdng thi trung tam cua qua trinh giao due lai la ngudi th^y Thdy cu- day nhung cai ma thay cd, thay tam dac; cdn ngudi hpc linh hpi tri thiic mot each thu dong nhd dpc - chep - hpc thupc Idng nhirng bai thdy da chuan bj nhu mot mlu cd san, nhieu liic khdng cap nhat vdi thuc tai dang sdi n6i dien ra tijrng gid, tijfng phiit ngoai ddi

Vdi each hpc truyen thdng, kien thuc ngudi hpc thu nhan duac khdng viing chac nen dan de'n kha nang van dung kieh thiic cua ngudi hpc kem, it linh hoat va khdng sang tao

7.7.2 Quan niem ve day hgc tich cue

Theo T.S Dang thanh Hung ''day hgc tich cue hay cdn gpi la day hgc

hudng vdo ngudi hgc, la'y chu the hpc sinh lam trung tam duac coi la thanh

tuu hien dai cua Au- My"[2l] Thuc ra, each day hpc hudng vao ngudi hpc da

cd tii thdi ky co dai Hy Lap duac Thay trd Platon va Arixtdt thuc hien d trudng

Academi Phuang phap day hpc nay duac cac dng gpi la ''Van ddp phdp'\

Cac 6ng rat ft khi tap trung sinh vien d giang dudng ldn, ma thudng dan timg top chuyen de viira di dao vira dam dao theo each Thay dat cau hdi, Trd dap, va

nguac lai Cii the soi noi khdng bao gid diit, moi van de tranh luan deu duac

ngudi hpc thau hieu mot each can ke Ngudi ddi gpi trudng phai nay la

"Trudmg phdi Tieu dao'\Nhcf phuang phap nay ma Thay Platon da dao tao ra

tro Arixt6t-Ngudi duac Mac gpi la:"B6 dc bach khoa toan thu ciia nhan loai thdi e6 dai" Khi trd thanh Thdy, Arixtdt da day hpc eho Alechxang Dai de-mot vi vua limg danh cua co dai

Nhu the, phuang phdp day hgc tich cue cd nguon gdc ttr xa xua, ban

than nd khdng phai la san pham rieng cua Au My ma la san pham ciia nhan loai Chi cd di^u, khi dd thi phat trien, xa hpi cong nghiep ddi hdi dao tao hang loat eae tri thiic cung theo kieu eong nghiep Viec md trudng 6 at vao thdi Phuc Hung ngudi ta da quen mat each day hpc tieh cue ciia ngudi xua Ngay nay, nhd cd su phat trien ciia cdng nghe thdng tin, ngudi ta lai cd dieu kien de

tac ddng vao timg thanh vien cua ngudi hpc hay cdn gpi la ''phuang phdp cd

biet hod ngudi hgc^\ Nhu vay, viec xem xet tudng tan lich sir su pham eho

phep ta ed cai nhin bien ehiing de tiep thu cd ke thira ma khdng roi vao phii dinh sach tran nhiing gia tri tdt dep eua truyen thdng va cung tranh duac thieu

sdt ki^u " cii ngudi mai ta'\ tu nhan mdt phat kien khdng phai ciia minh Xet toan cue ta thay, bdn chdt cua day hgc tich cue Id mgt qud trinh ngudi thdy

biet to chicc, dieu khien hgc sinh tu bien doi nhdmg kinh nghiem ben ngodi thdnh kinh nghiem ben trong cua cdc em, kem theo khd ndng biet van dung, sdng tao

Ndi mot each khac, chiing ta cd the eoi: Day hgc tich cue la kieu day hpc nham bien doi chdt lugmg tuduy cda ngudi hgc theo hai hudng:

a Tii tu duy dan tuyen, sang da tuyen( Complexus) theo chieu sau

b Tir tu duy thu dong, sang tu duy sang tao khong ngiing

Muon bien doi chat luang tu duy ciia ngudi hpc theo hai hudng tren cdn

cd phuang phap tdi uu de thuc thi nhiem vu dd

1.2.Phuang phap bien doi chat luang tu duy cua ngudi hoc

1.2.LMot sd khdi niem lien quan den tuduy

Cd r^t nhieu khai niem lien quan tdi tu duy Trong bdi eanh cu the cua de tai, e6ng trinh chi cd the xem xet nam khai niem lien quan tdi tu duy dd la:

Chu thi tu duy, ddi tuang tu duy, ban chdt tu duy, nang luc tu duy, kich thich

tu duy

a Chi4 the tuduy

Bdt cii m6t su ton tai nao trong thue te, deu la ton tai trong quan he, Cd mdt quan he ca ban nhdt lien quan den tu duy la mdi quan he giiia chu the

nhan thiic va ddi tupfng nhan thu'c

Trude bet ndi ve chu the nhan thdc, day la linh vuc chu quan, vi the ndi tdi chu the la ndi tdi chii the Ngudi, Trong qua trinh kham pha va bien ddi tu

nhien cung nhu bien doi xa hpi nhdm phuc vu cho loi ich cua minh, ehu the Ngudi quyet dinh kham pha nhung bi dn eua cupc sdng Budc ddu tien de kham pha nhirng bi an ay, chu the Ngudi quyet dinh van dung siic manh tdi thuang cua minh ma khong mot sinh vat nao cd the sanh kip, dd la siic manh ciia tri tue Sd dl ed su vuat troi cua chii the Ngudi so vdi cae sinh vat khac la

do eon ngudi bie't phat trien hai siic manh ca ban cua minh Ph.Angghen trong

tac pham Tdc dung cua lao dgng,, da nhan manh: "Trude het la lao dong; sau lao dong va ddng thdi vdi lao dong la ngon ngu; dd la hai sdc manh kich

thich chu ye'u da anh hudng den bp dc vuan, lam cho bp dc dd dan dan bien

chuyen thanh bp dc con ngudi" [11,102-103],

a Ddi tuang cita tu duy

Da CO mot su 1dm ldn ngay ca trong mot sd nha khoa hpc khi ddng nhat giira khach the va ddi tuang cua tu duy( ddi tuang nghien cm) Thuc ra khai niem khdch the la mot khai niem triet hpc de chi su tuang phan vdi chu the

Hai khai niem nay sanh ddi vdi nhau de phan biet giira chu quan va khach quan Cdn trong ITnh vuc tu duy, khdng cd mot nha khoa hpc nao lai lay khach the lam ddi tuang nghien cim vi nd qua rong va qua chung Chinh vi the, ngudi

ta chi ed the' xae dinh duac mdt pham vi nhdt dinh cdn thiet, cdp bach trong toan bd khach the duac tach ra de giai quyet Nhd dd, tu duy cd the xac djnh duac muc dich va pham vi nghien ciiu eua minh

Nhu vay khai niem Ddi tuang cua tu duy la mdt khai niem nhdm xac

dinh muc dich va pham vi nghien ciiu ciia tu duy Cd xae dinh duac ddi tuang cua tu duy dac biet trong linh vuc su pham, cdng trinh mdi cd ca sd de kich thich, bien doi va nang cao nang luc sang tao eiia tu duy

b Bdn chdt ctla tu duy

Tu duy la thanh qua cao nhdt, tdi uu cua mot hien tuang vat chat huu ca

dae biet ciia con ngudi - dd chinh la bg dc, Tu duy duac bieu hien ra thanh qua

trinh boat ddng cua su phan anh hien thuc khach quan vao ca quan dac biet dd

va duac eu the hoa thanh nhirng bieu tuang, nhiing khai niem, nhung phan doan, nhirng suy luan duac bieu dat bdng nhirng tir, ngir, cau, ky hieu hoac cdng thiic v.v Qua trinh tu duy bao gid cung la mot qua trinh gdn ket vdi nhiing hinh thiic nhat dinh eua su van dong vat chdt vdi hoat ddng cua nhiing naron thdn kinh eiia bp dc

Thdng thudng, ngudi ta hay thien ve quan niem coi tu duy la ca sd de de

ra tri tue, de ra kien thiic Nhu vay, tu duy mdi duac xem xet ve phuang dien ly tinh Thue ra, tu duy la ket qua eua mot tong hap giua cam tinh va ly tinh Bdt cir mot nhan thiic nao cung phai can cir vao tai lieu eua giac quan, sau dd nd

mdi dugc nhao nan thanh tri thirc Tren ca sd nay, chiing ta cd the cd dii eii

lieu de nghien ciiu ve dac diem cua tu duy trong day hpc Khac vdi tdt ea cac linh vuc khac, linh vuc su pham thudng bat ddu bdng viec tac dong vao hai cira

ngd {hai kenh) cua ngudi hpc, dd la thi gidc va thinh gidc, sau dd nd duac

truyen ddn mpi thdng tin ma ngudi hpc duac nghe thdy giang, duac nhin thdy viet, cung nhu mpi hanh vi, mpi phuang tien giao tiep tuang tac giua ngudi hpc

va ngudi day deu truyen ddn qua hai kenh nay Tren ca sd ciia nhirng khdng

dinh tren, cdng tiinh mdi cd du ea sd khoa hpc de tien hanh tim ra each thirc kich thich nang luc tu duy cua ngudi hpc

Nghien euu ban chdt eua tu duy chiing ta cdn phai chu y den tinh khdi

qudt cua tu duy nghla la tu duy phan anh nhung thude tinh chung, nhirng mdi

quan he cd tinh quy luat cua hang loat su vat hien tuang Tu duy cdn mang

tinh gidn tiep khi nd su dung ngdn ngu de phan anh (suy nghi bao gid cung

gdn ket vdi tir ngu ma nd cdn bieu dat chinh cai npi dung dd; bdi ngdn ngu

duac xem la phuang tien ciia tu duy) Tu duy cdn mang tinh triru tuang, vi tu

duy cd xu hudng thoat ly ndi dung mang tinh dac thii ciia su vat va hien tuang

cu the de khai quat ra nhung quy luat chung

c Ndng life tuduy

Mdi ngudi sinh ra trong mdt hoan canh nhat dinh, vdi mot truyen thdng nhdt dinh, tham chi vdi mot bp zen nhat dinh, vi the de ra nhirng nang luc tu

duy khac nhau Nghien ciiu nang luc tu duy cdn phai tinh den 'kho dir trir'

kie'n thiic cua mdi ngudi Day cd the coi la xuat phat diem khac nhau tao nen nhirng nang luc tu duy khac nhau

Xet toan cue, ndng luc tu duy cua con ngudi trude hit la nguon luc vdn

CO, la sire manh ben trong tgo nen khd ndng co the suy nghi, sdng tgo de hoan thdnh mgt nhiem vu nao do dem lgi hieu qud thirc tien Nang luc tu

duy la vi the nd ludn gdn ket vdi sang tao Sang tao la mat nang dong nhat cua tri tue biet to hop nhung vdn kien thiic da cd de phat huy tam phuang dien ciia

nd do la : Giao tiep, trai nghiem, Idgic, ng6n ngir, npi tam, nhac dieu, khong

gian, tu nhien Kha nang huy dong cang nhieu thanh td tren thi nang luc tu duy cang cao

Trong linh wlc su pham, van de phat hien nang lire tu duy ciia ngudi hpc,

biet each kich thich va bdi dudng tam phuang dien ciia nang luc tu duy ke tren

se lam cho viec day hpc dat hieu qua cao han

d, Kich thich ndng Ivrc tu duy

Trong eude sdng, khdng phai liic nao nao bp cQng boat dong tdt ca cae bp

phan Chinh vi vay ed vdn de thdc, ngu hap ly eua sir dieu hanh nao bd de dap

utig nhirng vdn d^ ciia nhan thirc ma vdn bao toan duac sire khoe eua con

ngudi W6 vdn de nay, nha triet hpc e6 dien noi tieng cua Diic Inmanuen Kant

eudi the ky XVIH da cho rdng : "Cai tinh hinh pham vi cae true giac va cam giac, cam tinh ma chiing ta biet tdi, mac du chiing ta diit khoat cd the khdng

dinh rdng ed, tire la (pham vi) cac bieu tuang m&nhgt d con ngudi (cQng nhu d ddng vat) la bet siic rong ldn, cdn nhirng bieu tuang ro rdng thi chi chiia dung

mdt sd luang het siic nhd be tren eae diem eua ehiing, cae diem duac hien len trude y thiic; cai tinh hinh tren tam ban dd to ldn eua tam hdn chiing ta, cd the

ndi la chi ed mot sd it diem duac rgi sdng ma thdi- chinh la mot tinh hinh cd

the ddy nen d chiing ta sir ngac nhien trude thuc chdt cua ban than ehiing ta, Chang vay ma neu nhu mot siic manh thuang dang nao dd ndi: se cd anh sang, thi chang cdn mdt tac dong rdt nhd be nao tir phia chiing ta cung vdn hien ra trude mdt ehiing ta mot nira the'gidi : [l 9,366] (Inmanuen Kant Toan tap, Nxb

Tu tudng, Matxcova, 1966, tap 4, tr366)

Nhu vay, qua ly thuyet eiia I Kant cd van de vdng sdng va vung tdi

(mien thiic va mien ngii) trong nao bp eiia chiing ta Dieu nay la diing, bdi ne'u nao bp chiing ta sang tnmg he't thi ed nguy ea benh ly, Cung tii day, cd the nit

ra mot van de ly thii cua su pham hpc, dd la: day hgc chinh la mot qua trinh

kich thich nhirng mien ngu ciia tu duy ngudi hpc mot each hap ly theo mot

dinh hudng nhdt dinh cd lai cho viec nang cao trinh dp va phat trien nang lire

tu duy cua ngudi hpc Trong thuc te, cd khong it ngudi day da khong y thiic duac dieu nay, nen nhung gid day cua hp v6 tinh da bien thanh gid ru ngu ngudi hpc

Tir nhiing ea sd tren, dac biet tir ly thuyet eua L Kant, ta ed the khdng

dinh rdng : kich thich ndng luc tuduy chinh la mgt chudi tdc dgng suphgm

vdo nguon luc vdn cd, vdo sdc manh ben trong cua ngudi hgc dang trong trang thdi nghi de lam cho nd bitng tinh nhu cdp them ndng lugmg vd da lieu de cho nd phdi hap cdc phuang dien Idgic tri tue nhdm gidi quyet nhirng vdn de dang ddt ra cho chu the nhdn thdc

1.2.2.Mgt so phuang thuc ton tai cda tu duy

Theo Heghen, Tu duy la mdt qua trinh van ddng cua nao bp de nhan thire

va kham pha ehan ly Chinh vi vay, tu duy cd ba kieu tdn tai ea ban dd la: Tu

duy khoa hgc thong qua van dung cae khai niem de kham pha chan ly cua cdi dung, Kieu tu duy dac tnmg eho nhan thiic tdn giao de kham pha niem tin

duac tong hap va cd dinh vao mot bieu tugng Kieu tu duy hinh tuang cam

quan sinh dong (chinh la dac trung cua nhan thirc nghe thuat) Trong khuon kh6 ciia cdng trinh nay, chiing toi chi di vao nghien ciiu kieu tu duy khoa hoc

va tu duy hinh tuang

a Tuduy khoa hgc

Tu duy khoa hpc la kieu tu duy lay khai niem lam c6ng cu Khai niem la san pham cua boat dong tu duy Bp dc con ngudi sang tao ra cac khai niem nhd nit ra mot loat nhiing dac trung chu yeu cua sir vat, hien tuang qua phuang thiic khai quat cao, Chinh vi the, tdt ea cac khai niem khoa hpc deu mang theo tinh chat la nhiing mo hinh eiia hien thuc ma nd phan anh Tu duy khoa hpc xudt phat tii su lien ket cac khai niem da bie't de phdi hap trong kham pha cac hien tuong chua biet; dua nhiing hien tuang chua biet cdn cd tinh chat ngdu nhien va Ion xpn vao he thdng de phat hien ra nhirng quy luat khach quan Sau

dd con ngudi da sir dung nhiing quy luat dd vao boat dong thuc tien nhdm dat hieu qua tdt nhat

Siic manh cua tu duy khoa hpc la nhiing thanh tu khai quat cua nd Tir dd,

nd thiic day sir hinh thanh ky thuat, Nhd ky thuat, khoa hpc lai cd dieu kien

tiefn len vd md ra nhiing muc tieu nghien ciiu mdi, nhirng yeu cdu chan ly mdi, Thi du: nhd ky thuat ten lira va may dien toan, con ngudi cd the dua kinh vien vong vQ tru len quy dao Lai nhd kinh vien vpng vu tru, eon ngudi cd the quan sat chup hinh nhilu hanh tinh mdi Tu duy khoa hpc cdn duac coi la tu duy

duy ly, chii yeu dua vao ly tinh, Idy nhiing phan doan, nhirng dinh de de phat

dong nhan thure

Kieu tu duy khoa hoc thuc chdt la kieu nhan thirc da tuyen.Tu duy da

tuyen cd dac diem la bao quat tong the ddi mdi su vat, nhung tir dd nd lai ndm duac ban chdt sau xa ciia sir vat Khdng cd sir vat nao ton tai cd lap, dan gian, chi mot b6 phan, mot phuang dien ma khong cd quan he qua lai tren nhieu

binh dien Tu duy da tuye'n trong khoa hpc cdn gpi la tuduy tuang tdc theo he

hinh Trong giao due hpc, tu duy khoa hpc la nen tang, la hat nhan cua qua

trinh tuang tac giira ngudi day va ngudi hpc Sir hinh thanh va phat tri tue deu phai dua tren kieu tu duy khoa hpc

b Kieu tuduy hinh tuang

Tu duy khoa hpc tuy ddng vai trd ehu dao trong nhan thire, nhung nd mdi chi la mot nua eiia nhan thiic Mae da timg nhan manh: " kh6ng phai chi d

trong tu duy ma bdng tat ca cac gidc quan, con ngudi do dd da tdn tai rd ret

trong the gidi khach quan" [l 1,103 -104]

Nhu vay, Mac cho rdng, muon tdn tai va phat trien trong the gidi khach quan, con ngudi cdn phai biet huy ddng tdt ea cac phuang dien nhan thiie Ngoai nhan thiic khoa hpc, con ngudi cdn phai biet huy dong kha nang nhan thu'c cam quan sinh dong

Diing nhu vay, xet ve mat lieh sir, thi tuoi ddi cua cam quan sinh dong cd

be ddy han nhieu so vdi nhan thiic ly tinh Ph Angghen da cho chiing ta thdy

cii heu da duac tong ket nhu sau : " Trude khi manh dd ddu tien duac bdn tay

con ngudi Idm thdnh mot con dao thi bao nhieu thdi dgi dd qua roi, vd so

sanh vdi cdc thdi dai dd, thi thdi dgi lich sd md ta dd biet khdng thdm vdo ddu cd'\ Nefu so vdi cu6e ddi eua mot eon ngudi cu the, ta cung thdy quy luat

nay : ngay tii khi chua cdt tieng khde chao ddi, be da duac thira hudng ca mot

be ddy cam quan cua nhan loai da duac tieh tu va duac truyen lai eho be thong

ma zen cua cha me be truyen eho be

Qua diing nhu vay, neu ehi diing lai d tu duy ly tinh, qua de cao tu duy ly tinh trong giao due thi de rai vao phien dien, kieu giao due nhu the' cung de tao

ra con ngudi thieu ddng bp Trong khoa hpc giao due hien nay, ngudi ta khong chi nhdn manh den ehi sd thdng minh cua duy ly (IQ), ma cdn chii y den chi

sd nhay cam gpi la (EQ)

Trong thue te' cupc sdng cd biet bao nhieu trudng hap ne'u chi dimg duy ly thi khdng the nao giai quye't duac Ngudi cd tai cam nhan trude day d nude ta

la Trang Trinh Nguyen Binh Khiem khi Ong tang Nguyen Hoang hai cau tha:

Hodnh San nhdt ddi Van dgi dung thdn

Vdi trudng hap cua Nguyen Hoang trong xu the' dang xung dot mot mdt mot cdn vdi Trinh Kiem( anh re), Idi khuyen cd tinh du bao ciia Trang Trinh

Nguyen Binh Khiem: " Hay di vao day Hoanh san, se lap duac nghiep, se

dung than duac mudn ddi" Cung nhd Idi khuyen nay, vdi tai Nguyen Hoang, dng da dung len sir nghiep ldn eiia Chiia Nguyen (dang trong) va ed cdng ciing dan ta khai pha them duac vua liia thupc dong bdng sdng Cim Long, khien nude ta trd thanh nude xudt khau gao ldn thii hai tren the gidi

Ngudi cd tai du bao thii hai d nude ta phai ke den Hd Chi Minh Bac da

cd tdt ea 10 du bao thdn ky ve nhirng mdc quan trpng nhat lam bien doi cue dien each mang d nude ta Sau day la bdn du bao tieu bieu:

Du bao thii dau tien cua Bac ve chien tranh the gidi lan thu nhat vao thang 8 nam 1914, khi dd Bac cdn la chang thanh nien Nguyen Tdt Thanh

Tie^p dd d£fn du bao thii hai vao nam 1924 ve chien tranh the gidi ldn thir hai va thanh cdng tat yeu ciia Lien Xd

Du bao bao quan trpng thii ba vao thang 5 nam 1941 tai hpi nghi Trung uong d Pdc Bd, Bac da du bao ve viec chuan bi ddn thdi ca tong khdi nghia va sau dd, thang 2-1942, Bac qua quyet: "1945 - Viet Nam doe lap" Nhirng du bao thien tai nhu the" da khie'n Trung uomg dinh ra nhung dudng loi chinh sach dung [22-28](TulieucLiaAwn/w/i//?^'^/ofngay 14-5-2005 sd 421, tr 28) Tii dd cd the' nit ra quy luat, ngoai nhan thiic ly tinh, con ngudi cdn phai

huy ddng tdi da vai trd cua cdm nhdn, Trong giao due mudn dao tao duac

nhirng con ngudi manh ve ly tinh, gidi ve cam nhan, nen giao due dd se dao tao duac nhiing con ngudi toan dien chi ed nhirng con ngudi toan dien nhu the' mdi dap iing duac sir bie'n doi cua kinh te thi trudng - nen kinh te bien doi theo timg gid timg phiit Nhieu dan toe bi thua kem dan toe khac cung cd khi chii ye'u la do trinh dp cam nhan kem

Nhu vay, thuc chdt cua giao due la biet huy dong siic manh tdng the cua

nhan thiic con ngudi ve hai phuang dien ly tinh va cdm nhdn Mudn lam duac

dieu nay phai cd phuang phap, ma phuang phap chii ye'u la phuang phap nang cao nang luc tu duy cua ehu the tie'p nhan Ndi mot each khac, day ciing chinh

la hudng di tim phuang phap kich thich nang lire tu duy cho ngudi hpc

7.2.3 Phuang phdp bien ddi chdt lugng tuduy cua ngudi hgc

Mudn sir dung nhiing phuang phap hiru hieu de thuc thi su bien doi chat luang tu duy ngudi hpc, chiing ta cdn tim hieu ban chat giao due

Ve thuc chat, giao due va day hpc la mot hoat dong xa hpi nhdm khai md

va phat trien trinh dp dan tri bdng to chirc truyen dat va linh hpi tri thiic cung nhu kinh nghiem quy bau cua nhan loai, cua dan toe va thdi dai de cac ca nhan bien chiing thanh vdn ben trong eua ban than; tir dd hp cd the dap iing yeu cdu phat trien eua cupc sdng mot each tdt nhdt

Ngay nay, qua nghien ciiu cdn biet them mot khia eanh rdt quan trpng

ciia giao due dd la: giao due cdn ed nhiem vu thuc hien tiet kiem sinh luc de

dat duac hieu qua cao trong lao dong san xudt, dd la quy luat sdng da tdn tai hang chuc van nam trong cong ddng nhan loai Day la quy luat di tdt, ddn ddu, khdng bi lang phi trong lap lai De lam duac dieu nay, cac the he thudng tim each truyin lai tri thiic va kinh nghiem da tich liiy duac eho the he sau de khdi lang phi sinh lire; Ddy chinh la nguyen nhan ca ban de ra boat dong giao due ndi chung va day hpc ndi rieng

Nhu vay, muc dich giao due bao gid cung cd ngudn gdc tii nhu cdu xa hpi

va dac biet nhu cdu hudng tdi cua tiing eon ngudi mudn thuc hien nhirng muc

dich ca nhan trong muc dich cua dan toe: " xay dung mot xa hpi dan gidu nude

manh, eong bdng, dan ehu, van minh" Xu hudng phat trien ciia toan xa hpi hien nay la xu hudng vuan tdi kinh te' tri thiic- mot nen kinh te' chdt lucmg cao,

Chinh vi the, nen giao due cua ehiing ta hien nay cd nhiem vu la gia tdng ndng

luc tri tue cho ngudi hgc (nang lire ea bdp thi cd han, cdn nang lire tri tue ciia

con ngudi la v6 tan), Cd rat nhieu con dudng de phat trien nang luc tri tue cho the' he tre, nhung giao due - dao tao vdn la con dudng chinh, con dudng truyen thdng cua nhan loai tir xua den nay

Trong giao due dao tao, van de cdp bach dang dat ra hien nay la vdn de

phuang phdp dendng cao ndng li/c tu duy ngudi hgc Vi the chiing ta phai

nghien ciiu sau them ban chdt eua phuang phap,

Bdn chdt cua phuang phdp trong ddi sdng vd trong khoa hgc

Cho den nay van cdn khdng it Thay Cd giao va cac nha Khoa hpc chua

thdng nhdt vdi nhau vk vdn de " The nao la phuang phap Cd ngudi coi

phuang phap la each thue lam viec Cd ngudi lai ddng nhat phuang phap vdi giai phap, vdi nguyen tae lam viec Do dd cdng trinh thay can lam rd van de nay mot each thuc sir khoa hpc:

17 DAI HOC Q U O C G\P ^A NO

Mpi boat dong trong ddi sdng thuc tien va khoa hoc dhu rdt can den

phuang phap Phuong phap anh hudng true tilp din lai ich, chdt lugmg, hieu qua ciia qua trinh boat ddng Phuang phap cdn kieh thich tu duy con ngudi sang tao, chdng sir dan dieu nham te Da cd nhilu nha khoa hpc ndi ve vai trd

va ban chat cua phuang phap

Nha toan hpc Descartes da ndi rdng: "Thd dimg mong di tim bdt cir mot

chdn ly nao cd, cdn han lam viec dd md khong co phuang phdp'\

Nha tuomg lai hpc Thiery Gaudin da ndi rang: "//ay hoc phuang phdp chir

dimg hoc dir lieu "

Nha vat ly hpc A Poangeare eho rdng:

" Phuang phdp la khoa hoc lua chon buac di cua noi dung'\

Ngudi ed cdng ldn nhat trong van de nghien cim phuang phdp phai ke den Heghen Ong dua ra mdt djnh nghia rat chuan ve phuang phap:

- Phuang phdp la y thue van ddng npi tai cua ban than npi dung

- Phuang phap la cai thuc day su tien trien eua ndi dung

- Phuang phap la linh hdn khdi niem cua npi dung

Phan tieh nhimg quan diem tren, ta thay:

- Dieu kien de ed phuong phap la phai ed muc dich vd ngi dung

- Khi da cd muc dich, ndi dung thi nhiem vu eua phuang phdp la tim

cac giai phap de chuyen tai npi dung tdi ngudi hpc mdt each cd y thirc

- De tim ra cac giai phap tdi uu ddi hdi phai huy ddng tu duy, tao nen sir tu y thirc cua ngudi dieu khien boat ddng ndi dung, trong mot hoan cdnh cu the

Di sau vao phuang phap gido due, ta thay nhiem vu chu yeu eua thay vd trd la phdi tim ra phuang phap tich cue de kich thich nang lire tu duy ciia ngudi hpc nhdm dao tao ra nhirng nhan lire tri tue bac cao

Vay phuang phdp tich cue Id gi?

Phuang phdp tich ctrc la phuang phdp tao ra sir ehu ddng cho ddi tuomg

de ddi tuomg boat ddng dat ket qua cao vdi tdc dp nhanh Ndi each khde,

phuang phdp tich cue cd tdc dung thuc day boat ddng cua ddi tuomg theo

hudmg phat huy ndng luc ngi tai ciia hp Phuang phdp tieh cue khdng ehi ed

tac dung dem lai nhieu tri thirc mdi, md cdn ed tae dung lam bien ddi nang lire

tu duy cho ngudi hoc Mudn lam bien ddi nang lire tu duy eho ngudi bpc thi

phai cd phuang phdp kich thich ndng luc tu duy do

Kick thich la mdt qua trinh tdc ddng bang mdt loat cae yeu td ed dieu

kien nhdm tao ra nhirng chuyen bien tich cue d ddi tuang de dat dupe mot

SO yeu cau nhat dinh Kieh thich ndng luc tu duy vi vay la mdt qud trinh tdc

ddng bang mdt loat cac yeu td ed dae tnmg thupc linh vuc tinh than cua ddi tuomg De kich thich nang lire tu duy eho ngudi hpc, ngudi day phdi biet tao nen bdn phuang dien tinh than trong ngudi hpc, dd Id:

- Tao cho ngudi hpc niem say me, himg thu qua boat ddng hpc tap,

- Lam eho ngudi hoc nhan rd hanh phuc, tuomg lai cua ban than phu thude ed tinh chat quyet djnh vao trinh dp hpc van va eae tri thire ed duac qua boat ddng hpc tap eua hp

- Tao ra kha nang biet nd lire cd nhan d ngudi hpc, khd nang khac phuc nhimg lo hdng kien thirc eiia minh qua boat ddng hpc tap,

- Timg budc lam cho ngudi hpc biet ket qua cua nd lire ed nhan dupe bilu hien thanh budc tien trong trinh dp tu duy cua chinh hp,

Mudn kieh thich bdn phuong dien tinh than cua ngudi hpc, ngudi day can chii y tdi eae dieu kien: Nang lire ngudi hpc, nang lire ngudi day, ndi dung day hpc, mdi trudng vd trinh dp van minh eua thdi dai

Nang lire ngudi hpc Id mot khdi niem khdng dan gian Dd la mot td hap cau true da tuyen cd the ke den cdc thdnh td trong cau tnic dd nhu sau:

a Nang lire la trinh dp ngudi hpc dat den mdt hpc van nhat dinh

b Nang lire la khat vpng, y ehi vuom len eiia ngudi hpc san sang ddn nhan kien thue mdi,

c Nang lire la khd nang bien Tri thdnh Hdnh tire la biet dimg vdn tri thirc

da thu nap dupe de gidi quyet cdc yeu cau thue tien theo luat tdi im Nhu vay, nang lire la khd nang ben trong ciia mdi con ngudi, kha nang tao

ra mot sue manh vugt trdi vdi nhdm, vdi cdng ddng, biet lam cbii ban than va loi cuon ngudi khac vdo boat ddng dat hieu qua cao, Chinh vi the, dimg trude boat ddng day hpc, ngudi thay khdng the khdng xem xet den ngudi hpc dang d khdi dilm nao, eae vdn tri thire eua hp ed du de tiep nhdn nhimg kien thue mdi hay khdng ? Ngodi ra, ngudi day cdn phdi biet ngudi hpc cd khat vpng,

cd y thue trach nhiem mudn vuom len tiep nhan nhimg hieu biet mdi nhu the nao?.Tat ea nhimg can cir tren Id co sd khoa hpc giup giao vien tim ra phuang phdp day hpc eho phii hap vdi ngudi hpc de dat dupe hieu qua cao

2.Nang luc ngudi day

Can de phdng xu hudng mudn ha thap vai trd cua ngudi day Cau ndi

" khong thdy do may lam nen^^ ciia ngudi xua van cdn gid tri Trong gido due,

ngay nay ai ciing nhd den thdy Platon, thdy Arixtot cua thdi eo dai Hy Lap vd thay Chu Van An ciia Viet Nam Mudn cd trd gidi thi trude bet phdi ed thay

gidi (Pham Vdn Dong

Trong qua trinh day hpc, ngudi thay ludn di ciing vdi ngudi hpc, dam nhiem vai trd hudng dan, giiip dd ngudi hoc thu nap nhiing kien thirc mdi vdo kho tang tri thire eua hp Ngudi thay phdi la ngudi ed ba loai vdn ldn;

- Vdn tri thue chuyen mdn vuat cap so vdi ngudi hpc

- Vdn kinh nghiem su pham dat den mdt nghe thuat gidng day bac cao

- Vdn md rdng tri thiic, gpi md cdm hung sang tao cho ngudi hpc

a Von tri thirc chuyen man vuat cdp

Trude day d nude ta, thay cap III day trd cap II Thay cir nhan trd dai hpc

Trong gido due liic dd cd cau ndi vui ve trinh dp thay trd Id trinh dp " cam

cham cam"", Ngay nay, mudn day tieu hpc cung phdi ed trinh dp cao dang, dai

hpc trd len U trudmg Dai hpc Su pham da cd khoa " Dai hpc tieu hpc" Cdn d

cdc trudmg dai hpc, hau bet cdc gidng vien phai cd trinh dp thae sT trd len Cir nhan gidi giii lai trudmg ehi dupe lam viec vu tra ly,

b Von kinh nghiem suphgm

Von kinh nghiem su pham la kha nang hudmg dan ngudi hpc tiep nhan, xu

ly cdc tri thirc linh hdi mdt each khoa hpc vd dat hieu qua cao Dan gian cd

cau" Thay gid, con hdt tre"', y ndi: thay lau nam mdi cd kinh ngiem day ngudi

hoc, Trdi vdi linh vuc nghe thuat, nghe si trude het phdi tre, dep, duyen dang

{Thanh - Huang - Sac)

Nhu vay trong linh vuc gido due, vdn kinh nghiem su pham tuy dupe trang bi trong nha trudmg su pham, nhung ehu yeu van la vdn tu cd md ngudi

thay tich luy duoc qua nhieu nam hdnh nghe O day, vdn kinh nghiem su

pham dugrc danh gia khdng chi bdi sd nam len lap eua ngudi gido vien, md

con bang ea sang kien, tam huyet nghe nghiep, y chi lien tuc vuom len cua

ngudi thay Vdn kinh nghiem su pham cdn mang tinh chat la mot an sd nam

trong long tu trpng eua ngudi thay Day la mot tam ly het sue quan trpng,

tham ehi ed tinh chat thieng lieng ddi vdi ngudi day; bdi khdng thay cd gido

nao lai mudn bj hpc sinh coi thudng Mudn vay, khdng cdn eon dudng ndo

khde Id phai gidi {gioi cd kien thuc chuyen mon vd nghiep vu su pham) Ddy la

mot ddng ea tu nhien xuat phat tir tan ddy long eiia ngudi day Chinh vi the,

de phan dau trd thanh gido vien day gidi, ngudi thay da phdi day cdng luyen

tap, tu hpc, tu nghien cim trau ddi chuyen mdn eiia minh vd tieh cue hpc hdi

ddng nghiep Nhirng Idp tap huan theo chuyen de hdng nam do Bd, sd Gido

t r

due td ehiie la mdt trong nhiing hinh thirc gdp vdo vdn kinh nghiem eua ngudi

day, nang cao nang lire eua ngudi day len khdng ngimg,

c Von md rong tri thirc, gai ma cdm hirng sdng tgo cho nguai hgc

Trong gido due ed mat von cue ky quan trpng eua ngudi day la "AAa

ndng md rong tri thuc, gai md cdm hirng sdng tgo cho nguai hgc^\ Vdn ndy

ed tdc dung ldn ddi vdi viec kieh thich nang lire tu duy cho ngudi hpc bdi

"Hpc di ddi vdi hanh" ma Hdnh Id sang tao,

Xderat, Nhd triet hpc Cd dai Hy Lap da luu y thay ed gido ciing nhu luu y

todn xa hdi nam chir: " Tri - Hdnh- Dire cong chinh'' Tri Id tri thirc ed duoc

do hpc tap; Hdnh la boat ddng van dung tri thiie vao gidi quyet cac tinh hudng

cu thi Due cong chinh la y thirc tuan thu nhimg luat le eua cdng ddng, y thirc

khdng dupe vi pham phdp luat, khdng anh hudng tdi ngudi khac khi thuc thi

hdnh ddng cua ea nhan Nam chir nay deu ddi hdi sir van dung sdng tao d mdi

ngudi

De gai md cam hung sang tao cho ngudi hpc, ngudi day can biet kich

thich kha nang tiem tang trong ngudi hpc; bdi le nhan thiic bdng ly tinh chi

dem lai mot sd vdn tri thiic nhat dinh, cdn cdm hiing dua din sdng tao lai song

hanh ben eanh nhan thiie ly tinh md ngudi ta quen gpi Id cdm nhgn.Xct ve

phuang dien nhan thiie, nhan thiic ly tinh ed thdnh tuu cao nhat mdi dat dupe

d the ky XVII thdi eiia Descartes vdi cau cham ngdn: " Toi tu duy, vay toi ton

tgi"; cdn nhan thiie bang eon dudng cam nhdn lai ed tudi ddi vdi be day hdng

trieu nam gan lien vdi tudi ddi eua ea nhan loai Chang the ma sau nhieu nam

tran tra kiem tim quy luat ve sire day eiia nude, Acsimet van ehua tim ra bang

eon dudng duy ly Nhung chi mot lan khi ngam minh trong bdn nude, Ong

•w r t 1

bdng cdm thay tir ben trong cdi sire day ky la tae ddng len co the eua minh, vd

cii the mdt each hdn nhien nhu tre nhd, Ong chay ra dudng va reo len:

"Oreca " (tim ra rdi), Tir dd dinh luat ndi tieng ndy mang chinh ten Ong: dinh

luat Acsimet

Xem the, ngudi day gidi la ngudi biet huy ddng d ngudi hpc ciing mot liic

hai loai tu duy:rw duy ly tinh vd tu duy cdm nhan Neu cap eho ngudi hpc todn

tu duy ly tinh thi ngudi hpc ed kha nang bat chude tdt, nhung sdng tao kem

Cam nhan ed the coi Wgidc quan thic sdu ", De ngudi hpc cd cam nhan tdt,

ngudi day can cd ndng luc tgo gai cdm, tgo say me (Passion), tgo hirng thu

cho ngudi hpc nghla la, trong bdi day phai tao dupe dm hudmg, tao ngpn lira

ben trong khdt vpng hudng thuang truyen den ngudi hpc Dieu nay trong gido

due eiia chiing ta cdn dang bd ngd,

2 Ngi dung day hgc

Npi dung day hpc gan lien vdi muc dich, nhiem vu eua cd ngudi day lan

ngudi hpc, Ndi dung day hpc chinh Id khdi lugmg, chat luong tri thiic can

chuyin vdo " kho tiip nhdn cua nguai hoc'' de hp thue thi nhiem vu thuc tien

eiia cupc sdng dat ra hoac sang tao cdi mdi, Chinh vi the, ndi dung day hpc

phai phii hgrp vdi nang luc sd trudng cua ngudi hpc; bdi neu khdng, nd se trd thanh vat can trong sir chuyen giao tri thirc giira ngudi day vd ngudi hpc Su khdng phii hap ciia ndi dung day hpc se 1dm cho ngudi hpc coi thudng, chu

quan {neu noi dung day hoc Id qud de) hoac 1dm ngudi hpc mat himg thu do khd khan trong tiep nhan( vi noi dung qud cao, qud nang) Mdt ndi dung day hoc phii hop vdi ngudi hpc can dupe xdc dinh theo nguyen tae " du&n chdn"'

nghia Id ngudi bpc ludn ludn phai ed dp ed gang, nd lire eua bdn than thi nhat dinh se dat dupe hieu qua cao trong hpc tap,

O nhd trudng phd thdng, ndi dung day hpc eae mdn hpc d timg cap, timg lap hpc da dupe Bd Gido due, Sd Gido due quy djnh theo chuomg trinh, sdeh giao khoa thdng nhdt trong todn qude Tuy nhien vdi mdi ngudi hpc, ndi dung

ay lai hoan todn khde nhau bdi tinh chdt cdc viing, cdc mien, tham ehi d trinh

dp vd nang lire eua mdi ngudi ngay trong cimg mot lap Do dd, mudn cd dupe npi dung day hpc tdt phii hap vdi ngudi hpc can ddi hdi nang lire sdng tao d ngudi thay 6 day, ndi dung day hpc dupe ngudi thay sdng tao qua nghe thuat dan dat hpc sinh tiep can van de, gidi quyet van de, van dung tri thirc cua minh vdo giai quyet tinh hudng thue tien mot cdch thdng minh, bieu qua Nghe thuat dy cd mdt siic manh nhu mdt hieu img 1dm bimg sdng tri tue ciia ngudi

hpc trong cdm nhan vdn tri thire vira mdi linh hdi d\xoc nhu nd Id vdn cua

minh, ngay trong tam khdm minh, md nay minh mdi phdt hien ra Chinh dieu

dd da khich le tinh tich cue, chii ddng hom nira eiia ngudi hpc tren eon dudng kham phd ehan ly da ed vd kilm tim chan ly mdi

4 Moi trudng day hgc

Trong cimg qua trinh day hpc cd ngudi day va ngudi hpc deu boat ddng trong mdt mdi trudmg nhdt dinh Mdi trudng d day don gian ed the hieu nhu "

Cd vai nuac'\ Tuy nhien, khdi niem mdi trudng da dupe Qudc hdi thdng qua

ngay 27/12/1993 trong luat bdo ve mdi trudmg cd ndi dung nhu sau: " Mdi

truang bao gdm cac yeu td tu nhien vd yeu td vat chat nham tao quan he mat

thiet vdi nhau bao quanh eon ngudi, cd dnh hudng tdi ddi sdng, san xudt, sir

ton tai, phdt trien cua con ngudi vd tu nhien"

Dinh nghla nay mdi ndi tdi khdng gian dia ly noi con ngudi sinh sdng

^ ' > f

ddng thdi ciing ndi den todn bd dieu kien vd co, hiiu ea lien quan den boat

, ^ ^ f I f

ddng sinh tdn, tu bdo tdn vd giao tiep cua ca the sdng Song, mdi trudng day

hpc khdng hodn todn nhu tren, bdi mdi trudng day hpc Id mdi trudng nhan

hgc vdn hod, Khdi niem moi trudng nhdn hgc vdn hod da dupe tap the tdc

^ f f

gia eudn Ca sa ly luan Vdn hod Mac- Lenin do ALAcnondop chu bien, bdn

dich Nxb Van hod 1983 tr75 viet nhu sau: " Mdi van hod Id mot tdng the dn

f f f 1^

dinh nhiing yeu td vat chat vd nhan cdch, nhd dd cdc cd nhan tdc ddng lan

nhau, ehiing dnh hudng tdi boat ddng khai thdc vd sang tao gid trj van hod, tdi

nhu cau tinh than, hiimg thii vd dinh hudng gid tri eua hp, Mdi trudng van hod

khdng chi la tdng the hop nhdt nhimg yeu td van hod vat the md cdn cd nhirng

con ngudi hien dien van hod." [l8]

Vdi CO sd ly luan tren, khi dat mdi trudmg day hpc vdo nhan hpc van hod

ta cd dinh nghla mdi " Moi trudng day hgc Id mgt tong the nhirng yeu to vat

chdt vd nhdn cdch O do thdy tro tuang tdc ldn nhau trong sudt qud trinh

chuyin giao vd khdm phd cdc kien thirc mai, vai gid tri ngay cdng gia tdng;

dong thai ddt nen tdng dgo dire de ddo tgo nhdn lire cd trinh do hgc vdn, cd

nhdn cdch cao dep.'' Trong khdi niem mdi trudng day hpc can chu y den dang

cap eiia mdi trudng, Ngudi hpc duoc hpc trong mdi trudng dang cap

cao{truang co danh tieng) tu nd se la ddng lire kieh thich nang tuc tu duy cua

ngudi hpc dk phdn ddu dam bao danh tieng cho trudng ciing nhu cho chinh

ban than hp Chinh vi the, trong ngdnh su pham ludn ludn cd nhu cau xay

dung cdc trudng ddng cap cao; tir dd tao nen mdt dp chenh can thiet de thiic

ddy sir phdn ddu cua cdc trudng vd ngudi hpc,

Trong thdi kinh te tri thiie vdi xu hudng todn cau hod, khd nang tu duy ciia con ngudi trd thdnh mot tdi sdn vd gid Nhung mudn cd dupe tdi sdn quy bau nay khdng phai de ddng, bdi tdi nang md con ngudi cd dupe ehi Id 1% do bam sinh, cdn 99% do lao ddng sdng tao.Vdi todn bd ca sd tren, viec tim tdi

va de cao phuang phdp kich thich ndng luc tu duy, bien nang lire tu duy trd thanh to chdt rieng eho ngudi bpc va biet dat to chdt do vdo bdi cdnh cua thdi dai van minh sd phai Id mgty thirc thudng true trong ddi mdi phuang phdp

day hoc hien nay

Chuang 2

MOI QUAN QUAN HE GIUA DAY HQC GIAI TOAN VOI SlT PHAT TRIEN NANG LJfC TCDUY

2.1 Ban chat cua day hoc giai toan d nha trudng pho thong

2.7.7 Tam quan trgng cda day hgc gidi todn a trudng pho thong

Mot trong nhiJng muc tieu cdt loi cua qud trinh day hpc d nhd trudng phd

thdng hien nay Id bdi dudng phdt trien nang lire tu duy lQ{Interlligence

Quotient) vd nang lire cam nhan EQ{Emotion Quotient) cho hpc sinh thdng

qua day cdc mdn hoe

Todn hpc duac coi la mdn hpc ed vai trd hang ddu trong bdi dudng phdt trien tri tue eho hpc sinh Trong day hpc todn d bac hpc phd thdng, gidi todn la mdt npi dung quan trpng gan chat vdi cdc kien thiic, ky nang todn hpc trong chuomg trinh d timg Idp, timg cap Thuc te day hpc toan ta thdy, bai tap toan dupe sii dung vdi nhieu y nghla khac nhau Mot bai tap cd the dung tao tien de xudt phat, gpi dong ca nghien ciiu hoac tham gia vao lam viec vdi npi dung mdi, tham gia vao ciing cd luyen tap hoac kiem tra ddnh gia ke't qud hpc tap cua hpc sinh

Vdi sir phan tieh tren, rd rdng mdi bai tap dat d thdi diem khde nhau cua qua trinh day hpc toan deu chiia dung mot each tudng minh hay an tang cac chiic nang, gid tri khac nhau Chiing ta cd the ndi rdng: "to chiic hieu qua viec day hpc gidi toan cd vai trd quyet dinh nang cao hieu qud chdt luang day hpc toan" bdi cdc y nghla sau day:

- Hoat ddng gidi todn giiip hpc sinh cung cd, van dung cdc kien thiie todn hpc vd ren luyen ky nang Day la ca hpi tdt nhat de tu duy ciia cdc em dupe phdt trien va bpc 16 kha nang sang tao nhd qua trmh dem nhiing tri thiic Todn hpc da duac trang bi vao gidi cdc bai todn cung nhu gidi quyet cac van de trong cupc sdng thuc tien lien quan tdi todn hpc, Hoat ddng tri tue nay da gdp phan

ren luyen cac em y chi vugt khd, diic tinh can than, ehu ddo, lam viec ed kl hoaeh, thdi quen xet doan ed can cii, ludn biet tu kilm tra kit qua cdng viec cua minh v.v

- Viec giai toan cdn gdp phan quan trpng trong gido due tinh cdm eua hpc

Tuy nhien, de phdt huy vai trd eiia day hpc gidi todn, dieu dd cdn phdi tinh den phuang phap, tinh den nghe thuat giang day eiia ngudi thdy Ngudi thdy phdi bie't khai thae triet de cdc phuang dien cd the cd cua bai todn, giiip cac em hiing thii, say me vdi hoat ddng tim tdi, khdm phd trong gidi todn, tir dd tao nen loi suy nghi kieu cdu tnic da tuyen trong tu duy hien dai eua hpc sinh Mudn vay, tnrdc he't ngudi Thay phdi cd nhirng hieu bie't diing ddn ve ca sd ly luan cua viec day hpc gidi toan Co sd dau tien cdng trinh mudn de cap den la cdc quan niem ve gidi todn vd day hpc gidi todn

2.7.2 Quan niem ve gidi todn vd dgy hgc gidi todn

6 trudng pho thdng, day hpc gidi toan la npi dung quan trpng trong day hpc toan Hoat dong gidi toan la boat dong khong he xa la ddi vdi chiing ta, nhung khdng phdi mdi ai da timg gidi todn hoac tham chi dang day todn deu

cd cung mot cdu trd Idi eho cdc cau hdi sau day: Bai Todn la gi ? The nao la giai todn? The nao la day hpc giai toan ?, Diem khac nhau ca ban ciia hai qud trinh giai todn va day hpc giai toan la gi?

Trong cac giao trinh cu ve phuang phdp day hpc todn, cac tdc gid hau nhu khong dua ra dinh nghla ve nhimg khai niem nay, Tuy nhien, qua dieu tra,

khao sdt, so sanh tai lieu, dam thoai true tie'p vdi gido vien gidng day todn, sinh vien su pham toan va bpc sinh pho thdng, chiing tdi thdy cd mot sd quan niem khac nhau sau day:

Quan niem ve bdi todn

a) Quan niem ve bdi todn ciia mot sdnhd khoa hgc

L Astobar: chia bai todn thanh bdi toan chiing minh vd bai todn tim tdi,

- Bai todn chiing minh menh de A tir gid thiet B la su ddi hdi mot day huu ban cdc menh de A,, A2, A3 A„ thoa man dieu kien:

i Menh de eudi ciing A^ cua day chinh la menh de A

ii Mdi menh de Aj cua day hoac la tien de, hoac Id dinh ly hoac Id dupe nit ra tir nhiJng menh de diing trude nd nhd mot quy tdc suy luan 16 gic,

- Bdi Todn tim tdi la ddi hdi tim mien diing eua hdm menh de

2 Nha todn hpc Gpolya cho rdng: Bdi toan dat ra sir cdn thie't phai tim kie'm mot each cd y thiic phuang tien thich hap de dat duac muc dich trong thdy ro rang nhung khong dat ngay dupe,

3 G.S Fanghanel khdng dinh: Bdi todn la sir ddi hdi hanh dong trong dd quy dinh: ddi tuang ciia hanh dong, muc dich ciia hanh dong, cac dieu kien cua hdnh dong

4 G.S Rubinstem lai quan niem: " Ve bdn chat, mot bai toan la sir phdt

trien bang Idi ciia mot van de"

5 T.S Trdn Van Vu6ng va Vu Dire Mai (Trudng DHSP Ha Npi II) quan niem mot each cu the ban:

Bai todn la sir ddi hdi dat duac mdt muc dich nao dd Muc dich neu trong

bai toan cd the la tap hap bat ky (cua cdc sd, cdc hinh, cdc bieu thdc.) su

diing ddn hoac sai lam eiia mot hoac nhieu ket luan Bai todn dupe phdt bieu

nhd thuat ngii cua linh vuc chuyen mon nhdt dinh gpi la bai todn ciia linh vuc

chuyen mdn dd Vdi each hieu nay, bai todn se ddng nghla vdi de todn, bai tap, cSu hdi, vdn de, nhiem vu

6 T.S Ha SI Ho lai cho rdng, ed sir khac biet giira bai tap va bai toan, giiia bai tap va vdn de Cd bai tap khdng la vdn de ma chi yeu cdu hanh dong Bai tap la bai toan da xir ly v^ mat su pham

b Mdt sdquan niem khde:

Theo nghla rong, bdi todn la bdt cii vdn de nao cua khoa hpc hay cupc

sdng cd vdn de dang dat ra cdn dupe giai quyet Vdi quan niem nay, vdn de trat

tu an toan giao thdng d cac thdnh phd ldn cung dupe coi la bai todn

Theo nghla hep ban, bdi todn la van de nao dd ciia khoa hpc hay cupc sdng

cd vdn de dang dat ra cdn duac gidi quyet bdng kien thiic vd phuang phdp cua Toan hpc

Vi du: Cae bai toan sd hpc, hinh hpc, dai sd vd cd nhirng bai tap trong sach gido khoa vat ly, hod hpc deu dupe coi la bai toan

(^ phuang dien cue hep, cdn cd quan niem cho rdng: Bdi todn la bai tap

trong sach gido khoa toan

Tir nhirng quan niem tren, chiing ta cd the rut ra bdn chdt chung cua mot

bdi todn khi dua tren ca sa cua tu duy cdu true dd Id: mdi bai todn deu phdi

cd ba thanh td ca ban:

- Dii kien ciia bdi toan( cdi da cho)

- An sd ( cdi phdi tim)

- Dieu kien cua bai toan {mdi quan he giita cdc difkien vdi dn sd)

Quan niem vegidi todn vd dgy hgc gidi todn

Cung nhu khai niem ve bai todn, qua dieu tra khdo sat chiing tdi thay: cd nhieu y kien khac nhau xung quanh khai niem gidi toan va day hpc giai toan,

Co quan niem cho rdng: Gidi todn la di tim phdn can tim ciia bai todn cdn dgy

hgc gidi todn la day cho hpc sinh tim ra dap sd cua bdi toan Vdi quan niem

nay qua trinh day hpc giai todn da chii trpng den ddp sd cu the eiia bai todn

Song quan di^m khac lai cho thdy: Gidi todn la trinh bay dupe Idi giai cua

bai toan da cho; cdn day bpc gidi toan la giiip bpc sinh biet trinh bay Idi bai

toan dd Vdi quan diiva nay, ngudi thdy da rdt chii trpng den viec day hpc sinh

"mdu loi gidi' cua cac dang todn

Nghien cuu hai quan niem tren, ehiing ta thdy cdc quan niem dd deu cd mdt sd han che' nhdt dinh vi chua ehi ra dupe mat tich cue, chu d6ng sang tao

cua hpc sinh thong qua boat dong gidi toan Tir ca sd dd, chung toi cd the de

xudt mot quan niem rieng ve gidi todn vd dgy hgc gidi todn:

Giai toan la mot hogt dgng tri tue tich cue cua chu //z/nhdm tim ra each

gidi quye't nhirng yeu cdu ddi hdi ciia bai toan va trinh bay dupe Idi gidi bai todn mot each phii hap vdi cdp hpc Cdn day hoc giai toan la boat ddng tri tue cua ngudi thdy nhdm dieu khien trd tu gidi dupe bai todn mot each sang tao Day hpc gidi toan theo quan diem tren khong chi cdn den nhirng kien thiic ngudi hpc da dupe trang bi ma ddi hdi mot n6 lire tich cue, tu luc trong tu duy cung vdi kha nang sang tao vd kinh nghiem da dupe tich luy eiia cdc em tir viec gidi cac bai toan trude dd Cdn phdi luu y rdng, de ren luyen nang lire vd tao hiing thii trong giai toan, bpc sinh nen tu minh tim ra Idi gidi bai toan hoac nhd Thdy gpi y de tu gidi quyet; dimg bao gid voi vang xem tnrdc Idi gidi bdi

todn Cdn ngudi thdy, mudn co dupe sir chii dong, virng tin trong day hpc gidi

todn, ngudi Thdy phdi tham gia vao qua trinh gidi todn vd hieu dupe sau sde Idi gidi bdi toan

Qua phan tich tren, chiing ta cang thay ro; viec hieu diing khai niem giai toan vd day hpc gidi toan cd y nghla quan trpng de gdp phdn nang cao hieu qua eua gid day dong thdi giiip chiing ta nhan ra diem khac nhau eiia hai qua trinh nay:

Giai toan Day hpc gidi todn

• Ngudi giai tu tim ra hudng

gidi quye't cho bai toan

• Hoat d6ng gidi todn diln

ra dpc lap

• Ngudi day dieu khien ngudi hpc tu tim ra hudng gidi quye't cua bdi todn,

• Hoat dong trong day bpc gidi todn mang hudng tap the

2.7.5 Cdc budc trong dgy hgc gidi todn

Vdo nam 1950, GPdlia dua ra tien trinh bdn budc gidi toan song song vdi nhimg thdnh tim ciia cdc nhd tam ly hpc da de cap den trong boat ddng nhan

G.Pdli dua ra bdn budc trong gidi todn

1 Tim hieu dau bdi toan{understand

theproblem)

1

2 Ke hoaeh gidi( devise a plan) 3.Thue hien ke hoach gidi(carry out the plan) 4,Kiem tra(verification)

2.2 Tac dong tuong hd giiia hoat ddng giai toan voi ren luyen, boi du-ong, phat trien nang luc tu duy cua hpc sinh

2.2.1.Ndng luc tu duy cdn thiet trong timg buac cua hogt dgng gidi todn

Budc 1: Tim hieu ddu bai todn

Tim hieu ddu bai todn la viec lam tnrdc tien trong qua trinh day hpc giai toan Mudn hpc sinh tu minh gidi quyet dupe nhirng yeu cau ddi hdi ciia bai toan ngudi giao vien cdn phdi lam cho hpc sinh ndm dupe y nghla npi dung cua bdi todn, xdc dinh dupe yeu td ca bdn ciia bdi todn ddng thdi biet the hien bai toan dudi mot hinh thiic ngdn gpn de hieu Cd nhieu each de tim hieu ddu bdi toan va chiing ta cung thdy rdng: mdi bai toan cu the dat d mdi cap hpc

khac nhau se co nhiing each tim hieu d^u bai khac nhau Thong thucmg de tim hi^u dSu bai toan, ngudi ThSy c^n phai biet hudng hoc sinh tdi cac cau hoi:

- Cai da cho, va cai c^n tim trong bai toan la gi?

- Co moi lien he nao giua cai phai tim vdi cai da cho?

- Dieu kien cd dii de' xac dinh dugc an khong? Thieu ? Hay thCra?

- Ddi vdi bai toan hinh hoc ndi chung, yeu cau HS phai ve hinh (nhdt Id

ddi vdi bdi todn hinh hgc khong gian) Sau khi ve hinh xong va the hien dugc

cac yeu td da cho, ye'u td c^n tlm tren hinh ve, liic dd hgc sinh se hieu rd bai toan hon Mdt dieu c^n luu y la: hinh ve phai mang tinh tdng quat, khdng nen

ve hinh trong trudng hgp dac biet

De dat dugc nhung yeu cau ndi tren trong budc tim hilu dau bai toan, ngodi yeu td tdc ddng bdi ngudi Thdy budc hpc sinh phdi cd nhimg khd nang

\ f

ve tu duy nhdt dinh

Budc 2: Lap ke hoach gidi toan

Lap ke' hoach gidi toan la xdc dinh trinh tu cho viec gidi quyet nhung ddi hdi cua bai toan, Ndi mot each khac la day cho hpc sinh tim ra nhirng budc di tie'p can each gidi cua bdi todn Cd rat nhieu each de tim ra Idi gidi bai toan Ngudi day ed the sir dung cac cau hdi phan tich di len, tong hap hoac cac phep suy luan, quy nap de giiip hpc sinh tu tim ra Idi gidi cua bai toan d budc nay, rdt cdn den thao tac phan tich bai todn da cho thanh nhieu bai toan dan gian han Hpc sinh phai huy dong kien thiic cd lien quan den nhirng khai niem, nhirng quan

he trong de toan, rdi lira chpn trong sd dd nhung kien thiic gdn giii han vdi nhirng dir kien cua bai toan Md mdm, du doan, thir xet mot vai khd nang, ke ca mot vai trudng hap dac biet; ddi khi cdn xet mot bai toan tuang tu hoac bai todn khai quat cua bai todn da cho

Mudn hpc sinh dat duac ke't qua trong day bpc gidi todn, cdn cdn rdt nhieu dg'n nghe thuat hudng ddn eua ngudi thdy Ngoai ra, hpc sinh cung phdi biet huy ddng nhiing kien thu:c sdn cd, biet tap trung suy nghi vdi Idng say me hpc hdi kham pha trong gidi toan

Budc 3: Thuc hien ke' hoach gidi toan

Hoat dong thuc hien ke' hoaeh gidi todn bao gdm: viec chpn mot cdch gidi

va trinh bay loi gidi bai todn de hie'u nhdt, phii hop nhdt vdi bac hpc Ldi gidi bai toan duac hieu la tap hap cac thao tae sdp theo thii tu de di den muc dich

yeu cau ddi hdi ciia bai todn Thao tac dd cd the la phep tinh ca ban, phep

dung hinh ca ban, hoac m6t day cdc suy luan

Cdn phai luu y rdng: Ciing mot vdn de nhung each trinh bay ldi gidi d mdi cdp la khac nhau Tuy nhien, du trinh bay theo each nao thi Idi gidi mot bai toan khdng cho phep cd sai Idm Yeu cdu nay cd nghla la ldi gidi bdi toan phai ddm bdo dd chinh xdc ve kie'n thiic, hap I6gic ve quy tdc suy luan, ng6n ngir dien dat trong sang Vdi nhirng ddi hdi tren, khdng the khdng can den cdc thao tdc tu duy cua ngudi gidi todn

Budc 4: Nhdn dinh, ddnh gid bdi todn

d budc ndy, ngudi gido vien cdn luyen cho hpc sinh cd thdi quen kiem tra

lai tiing budc gidi, xem xet ldi gidi cd phu hop vdi cap hpc khdng, dap sd eiia bdi todn cd hcfp ly hay khdng? Ben canh dd, can phdi ludn Iu6n giiip hpc sinh khai thdc phat trien bai todn theo nhieu hudng khac nhau hoac nit ra nhirng kinh nghiem cdn thie't mdi khi gidi xong mot bai todn, De 1dm dupe dieu dd khdng phdi Id de dang, bdi ngudi hpc ngodi kien thiic todn hpc eiia minh cdn phai huy ddng cae thao tdc tu duy: phan tich, tdng hpp, so sdnh, trim tuong hda, khdt qudt hda, dac biet hda, tuomg tu hda mdi cd the cho nhan bdi todn cdn gidi quylt cd dilm gidng hoac khac vdi bdi todn da timg gap ciing nhu

moi cd the sang tae duac nhirng bai todn tuomg tu hoac sdng tao ban bdi todn

nhung hp cung de dang ddnh gid tri thdng minh cung cdc ndng luc tri tue

qua hogt dgng gidi todn Mot hpc sinh dupe coi la thPng minh hay la ngudi ed

tu duy toan hpc tdt thudng dupe bieu bien qua boat ddng giai todn nhu sau:

- Cd su quan sat tinh te', mau phdt hien ra eae diem niit trong mdi bai toan

de gidi quye't theo chieu hudng hop ly, dpc ddo,

- Suy luan cd can cii, ro rang, nhdt qudn logic, cd dc td md va ludn mudn tim tdi cdi mdi

- Khd nang suy luan theo hai hudng xudi ngupc nhanh nhay,

- Tri tudng tuang phdt trien nen khd nang chuyen tir cu the sang khai quat hod rdt tdt

- Cd khd nang tu hpc va hiing thu vdi viec tu tim tdi cae bdi todn de gidi.Khd nang du kiln hudng gidi quyet mdi bdi todn cung nhu viec van cdc kiln thirc todn hpc trong gidi quyet mdi bdi todn la rat tdt

Nhu vay, tri thdng minh toan hpc chinh Id sdn pham cua kien thiic, kl nang toan hpc ma chii the ed dupe thdng qua boat dong trong mot he thdng tu duy ddc lap, sang tao Tinh d6c lap tu duy ciia chii the dupe the hien d khd nang chii ddng, tich cue, bie't quan sat tinh te cac bai toan, vdn de todn bpc gap phdi d^ mau phat hien, tim ra cdc mdu chdt; tir dd de xuat cdc each gidi quyet Tri thdng minh cdn the hien d khd nang sang tao cua mdi chii the thdng qua dc phe phan, nhan xet, danh gid nhirng each gidi da ed de lira chpn each gidi mdi d6c dao, biet each tu minh kiem tra va hoan thien vdn de dat ra, dac biet la cdn biet sdng tao vdn de mdi

Mudn phat trien tri th6ng minh cho hpc sinh, ngudi Thdy cdn thudng xuyen ren luyen cdc thao tdc tu duy todn hpc eho cdc em nhu phan tich, tong hap, so sanh, tuang tu, khai quat hda, triiu tuang hda, dac biet hda, he thdng hda V v Viec ren luyen tri thdng minh ndi tren cd the bang nhieu con dudng khac nhau nhimg con dudng tdt nhat van la con dudng thong qua cac boat ddng gidi toan

a Phdn tich, tdng hap trong hogt ddng gidi todn

•\ f f

Xet ve ban chat d gdc dp ly luan chung ta thay:

Phdn tich la mot thao tdc tu duy nhdm tach cac van de Idn thanh nhiing van

de nhd de timg budc gidi quye't cac van di nhd; sau dd gop lai giai quye't tong

the vdn de ldn

Tong hap la khd nang boat dong cua tu duy biet gop nhiing bp phan cua

khdch thi lien quan ciing chu de, cung he thdng lam thanh ban chat ciia su vat mdi

Trong boat ddng giai toan, phan tieh - tong hop cd mdi quan he mat thiet,

bo xung, dan xen vao nhau trong qua trinh tu duy thdng nhat de gidi bai toan

Phdn tich la ca sd de tim ra ldi gidi bai toan va thudng dupe tien hdnh

theo hai hudng: